Question

A statistics instructor recorded the grades of his students on the final exam. The grades are: 

65, 72, 85, 92, 60, 52, 75, 79, 80, 89, 50, 59, 95, 99, 89, 77, 62, 65, 67, 73, 85, 23, 89, 94, 97 

a. Construct a stem-and-leaf display. 

b. Describe the shape of the distribution. 

c. Deterinine the mode and median of these scores. 

d. What percentage of the students passed (at least a 70).

Answer 1

Shape of DATA :- Left skewed ( Asymmetric)

Passed percentage = (16/25)*100 = 64%

Answer 2

Answer 3

Answer 4

(A)

Stem and leaf plot:

2	3
5	0 2 9
6	0 2 5 5 7
7	2 3 5 7 9
8	0 5 5 9 9 9
9	2 4 5 7 9

(B)

Mean:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

The formula for the mean of a sample isBoth of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:=74.92

Median:

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. Sorting the data set for the values entered above we have:

23,50,52,59,60,62,65,65,67,72,73,75,77,79,80,85,85,89,89,89,92,94,95,97,9923,50,52,59,60,62,65,65,67,72,73,75,77,79,80,85,85,89,89,89,92,94,95,97,99

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 77.

mean=74.92

Hence,

If the mean is less than the median, the distribution is negatively skewed.

(C)

Median=77

Mode:

The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are

89

(D)Marks more than 70=72,73,75,77,79,80,85,85,89,89,89,92,94,95,97,99=total=15 students.

total students=25

students who are passed==60%

please rate my answer and comment for doubts.