Question

1. Consider the table of test scores below:

36	16	61	97	27
37	64	59	91	81
86	39	56	85	26
36	51	18	68	69
78	61	49	29	82

1. Find the Mean.
2. Find the Median.
3. Find the Mode.
4. Discuss which of these statistics you would use to describe this set of test scores and back up your choice with some reasoning from the book or from your notes.

Answer 1

(a)- The formula for the mean of a sample is =∑x/n

i.e. sum of all the data values and dividing that sum by the total number of data values.

so mean= 1402/25

= 56.08

(b) The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers

Since there is an odd number of data values in this data set, there is only one middle number. With 25 data values, the middle number is the data value at position 13. Therefore, the median is 59.

(c)-

The mode is the number that appears most frequently.If it has two modes, the data set is called bimodal

modes are = 36,61

(d)- The Median is the score that divides the grade curve down the middle.Half of the students score at or above the median.

so in this case median will be describes data in better way than other statistic (mode and mean) .

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