Question

The weights of some children in a cricket club are given ( in kilograms ) below .

36 , 42 , 30 , 38 , 46 , 32 , 44 , 34 , 40

a) What is the mean weight ?

b) What is the median weight ?​

Answer 1

Answer:

answer of A is 32

answer of B is 44

Answer 2

a) 38

• The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics. Depending on the context, whether mathematical or statistical, what is meant by the "mean" changes. In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values. The equation for calculating an arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used ( attachment )

b) 38

• The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers. Note that when calculating the median of a finite list of numbers, the order of the data samples is important. Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results. In the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. When the data sample contains an even number of values, the median is the mean of the two middle values. While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample. In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same. Given the same data set as before, the median would be acquired in the following manner:
• 2,10,21,23,23,38,38
• After listing the data in ascending order, and determining that there are an odd number of values, it is clear that 23 is the median given this case. If there were another value added to the data set:
• 2,10,21,23,23,38,38,1027892
• Since there are an even number of values, the median will be the average of the two middle numbers, in this case 23 and 23, the mean of which is 23. Note that in this particular data set, the addition of an outlier (a value well outside the expected range of values), the value 1,027,892, has no real effect on the data set. If however the mean is computed for this data set, the result is 128,505.875. This value is clearly not a good representation of the seven other values in the data set that are far smaller and closer in value than the average and the outlier. This is the main advantage of using the median in describing statistical data when compared to the mean. While both, as well as other statistical values, should be calculated when describing data, if only one can be used, the median can provide a better estimate of a typical value in a given data set when there are extremely large variations between values.