Question

The back-to-back stem-and-leaf plot below show exam scores from two different math classes. Which class has a greater mean score? Which class has a greater median score?

Class A                 Class B
1 5                4           2
1 6 8             5           4
5 7 7 9          6          1 6
6 6 7 8 9       7          2 5 6 6
1 2                8          0 0 4 8 9
1                   9          3 5 6 7


A. greater mean = class A greater median = class A
B. greater mean = class B greater median = class B
C. greater mean = class B greater median = class A
D. greater mean = class A greater median = class B

Answer 1

The answer is letter B.

Answer 2

B. greater mean = class B greater median = class B

Explanation:

Stem and Leaf Plots : It is a special table where each data value is split into a stem (the first digit or digits) and a leaf (usually the last digit).

So, in the given plot for class A

The first stem 4 has leafs = 1,5

The numbers will be 41,45

The second stem 5 has leafs = 1,6,8

The numbers will be 51,56,58

The third stem 6 has leafs = 5,7,7,9

The numbers will be 65,67,67,69

The fourth stem 7 has leafs = 6,6,7,8,9

The numbers will be 76,76,77,78,79

The fifth stem 8 has leafs = 1,2

The numbers will be 81,82

The sixth stem 9 has leafs = 1

The number will be 91

So, The data of class A = 41,45,51,56,58,65,67,67,69,76,76,77,78,79,81,82,91

Thus MEAN of class A = Sum of all scores scored by students / Total No of students whose marks are given

⇒
`(41+45+51+56+58+65+67+67+69+76+76+77+78+79+81+82+91)/(17)`

`(1159)/(17)`

`68.17`

Thus mean of class A = 68.17

Median =The "median" is the "middle" value in the list of numbers.

Since 9th term is the middle value .

So, MEDIAN of class A = 69

The given plot for CLASS B :

The first stem 4 has leafs = 2

The numbers will be 42

The second stem 5 has leafs = 4

The numbers will be 54

The third stem 6 has leafs = 1,6

The numbers will be 61,66

The fourth stem 7 has leafs = 2,5,6,6

The numbers will be 72,75,76,76

The fifth stem 8 has leafs = 0,0,4,8,9

The numbers will be 80,80,84,88,89

The sixth stem 9 has leafs = 3,5,6,7

The number will be 93,95,96,97

So, The data of class B = 42,54,61,66,72,75,76,76,80,80,84,88,89,93,95,96,97

Mean of class B =
`(42+54+61+66+72+75+76+76+80+80+84+88+89+93+95+96+97)/(17)`

⇒
`(1324)/(17)`

⇒
`77.88`

Thus mean of class B is 77.88

Median of class B = 9th term = 80

Hence , mean of class A = 68.17 and median of class A = 69

Mean of class B = 77.88 and median of class B = 80

Thus Option B is correct .

Greater mean = class B

Greater median = class B