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Now that we have a way to calculate https://1investing.in/, we can compare the values obtained rather than shapes. The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler has taken 5 wickets each. The median number of wickets taken by the bowler in a match is __________ .

• The chart below depicts how a normal distribution looks like – resembling a bell-shaped curve that is spaced evenly on either side of the mean (µ), which is represented by the vertical line.
• The normal distribution is found to have a kurtosis of three.
• That is, while most returns are likely to be close to the market as a whole’s average return, yields often deviate widely from the mean.
• Well, to find that out, we need to convert daily mean and standard deviation to monthly figures.

Has been provided alongside types of What curve representaion of sample Mean or – 3 standard deviation a) leptokurtic b) platykurtic C) mesokurtic? Theory, EduRev gives you an ample number of questions to practice What curve representaion of sample Mean or – 3 standard deviation a) leptokurtic b) platykurtic C) mesokurtic? The normal distribution is found to have a kurtosis of three. A distribution with kurtosis greater than three is leptokurtic and a distribution with kurtosis less than three is platykurtic. For a distribution that is perfectly symmetrical, the mean will be equal to the median and the mode . However, if the distribution is asymmetrical, the mean will be either above or below the median and the mode.

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In short, a positively skewed distribution will have a tail that stretches to the right, while a negatively skewed distribution will have a tail that stretches to the left. The image below shows distributions that exhibit positive skewness, zero skewness, and negative skewness. A leptokurtic distribution has higher kurtosis and fatter tails.

## Measures of sample skewness and kurtosis

A leptokurtic distribution is one that has kurtosis greater than a mesokurtic distribution. Distributions of data and probability distributions are not all the same shape. Some are asymmetric and skewed to the left or to the right. Another feature to consider when talking about a distribution is the shape of the tails of the distribution on the far left and the far right. Kurtosis is the measure of the thickness or heaviness of the tails of a distribution. A measure of kurtosis indicates the degree to which the curve of a frequency distribution is peaked or flat topped.

Furthermore, a moderate level of platykurtic skewness suggests that the returns of Tata Motors are right-skewed. What curve representaion of sample Mean or – 3 standard deviation a) leptokurtic b) platykurtic C) mesokurtic? The Question and answers have been prepared according to the Commerce exam syllabus.

Some investors, on the other hand, are actively seeking leptokurtic return investments, anticipating that their extreme positive returns will outweigh their extreme negative returns. This is the reason most of the cautious investors may, therefore, avoid investing in leptokurtic markets and concentrate on investments that deliver platykurtic returns. On the other hand, some investors are actively seeking leptokurtic return investments, assuming that their extreme positive returns would more than balance their extreme negative returns.

That is, while most returns are likely to be close to the market as a whole’s average return, yields often deviate widely from the mean. Such dramatic and unpredictable incidents, also called “black swans,” are less likely to occur in platykurtic markets. You might have heard of the term ‘bell curve’, a curve that resembles the shape of a bell when plotted on a chart. In statistics, bell curve is frequently used to illustrate normal distribution, which is a type of statistical distribution that is symmetrical about its mean. The chart below depicts how a normal distribution looks like – resembling a bell-shaped curve that is spaced evenly on either side of the mean (µ), which is represented by the vertical line. A distribution with negative excess kurtosis is called platykurtic.

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Unlike skewness, which distinguishes extreme values in one tail from those in the other, kurtosis assesses extreme values in both tails. Tail data exceeds the tails of the normal distribution in distributions with strong kurtosis. In the above table, notice that Tata Motors had the highest standard deviation as well as the highest excess kurtosis. This means that since the start 2021 till the time of writing, compared to the other two stocks, Tata Motors not only had higher dispersion around the mean return but also had longer tails.

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Kurtosis is a measure that refers to the peakedness of the top of the curve . Kurtosis gives the degree of flatness or peakedness in the region about the mode of a frequency distribution. Based on the above, what do you think will be the range of returns for Nifty over the next one month, which is roughly equivalent to 21 trading sessions? Well, to find that out, we need to convert daily mean and standard deviation to monthly figures. Some researchers believe that investors should prefer positive skewness and should avoid negative skewness.

## Beta

Kurtosis is typically measured with respect to the normal distribution. A distribution that has tails shaped in roughly the same way as any normal distribution, not just the standard normal distribution, is said to be mesokurtic. The kurtosis of a mesokurtic distribution is neither high nor low, rather it is considered to be a baseline for the two other classifications. In a similar manner, one could calculate the potential range of returns for Nifty for any other period, such as for the next 1 session, next 1 week, next 1 quarter, next 1 year etc. Knowing the probabilistic range of security returns based on mean and standard deviation can help in making assumptions about the expected future returns of a security as well as in gauging potential risks. Based on one’s risk tolerance, it can also help in stock screening and selection.

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Based on the above table, let us now calculate the possible range of log returns within which Nifty could trade over the next one month. SSC CGL 2022 Tier I marks will be available from 28th February to 13th March 2023. The final answer key for Tier I exam has been made available on the commission website from 27th February 2023 to 13th March 2023.

When accompanied by low to moderately positive skewness, such distributions would imply at stable returns and low risk. This sort of distribution is something that would suit a conservative investor. Though mesokurtic distributions have a kurtosis of three, the positive and negative excess kurtosis in it are of the leptokurtic and platykurtic distributions respectively.

If the outliers lie above the mean, the distribution will be positively skewed . In this case, the mean will be greater than the median, which in turn will be greater than the mode. On the other hand, if the outliers lie below the mean, the distribution will be negatively skewed . In this case, the mean will be less than the median, which in turn will be less than the mode.

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More risk-averse investors may prefer platykurtic-distributed assets and markets because those assets are less likely to yield severe results. Compute the possible value of fourth central moment for the distribution to be mesokurtic platykurtic, and leptokurtic. Solutions for What curve representaion of sample Mean or – 3 standard deviation a) leptokurtic b) platykurtic C) mesokurtic? In English & in Hindi are available as part of our courses for Commerce.

In such a case, skewness and kurtosis would better represent risk. A leptokurtic distribution, in which excess kurtosis is positive, is the polar opposite of a platykurtic distribution. A leptokurtic distribution accompanied by negative skewness (left-tailed distribution) implies at a greater risk, because of the higher odds of negative outliers. On the other hand, a leptokurtic distribution accompanied by positive skewness (right-tailed distribution) implies at a higher odds of positive outliers. This sort of distribution is something that would suit an aggressive investor. Meanwhile, for return distributions that are platykurtic (short-tailed distribution), the outliers would be smaller than those found even in normal distribution.

Kurtosis is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. The peak is the tallest part of the distribution, and the tails are the ends of the distribution. The first four central moments of frequency distribution are 0,4,-2 and 2.4.

Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free. To answer these kinds of questions we need not just a qualitative description of kurtosis, but a quantitative measure. The formula used is μ4/σ4 where μ4 is Pearson’s fourth moment about the mean and sigma is the standard deviation.