Question

This following table given the frequency distribution of quiz marks obtain by first year student in Stat222
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Marks: 9,6,5,3,8,4,7.
Freqcy:2,8,y,6,4,y-2,6.
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If the mean mark is 5.5
(i) find the value of y,
(ii) calculate the median and mode of the distribution.

Answer 1

Answer:

y = 9

mode = 5

Step-by-step explanation:

Marks: 9,6,5,3,8,4,7.

Freqcy:2,8,y,6,4,y-2,6.

Total Marks =  9*2  + 6*8  + 5y  + 3*6  + 8*4  + 4(y-2)  + 7*6

= 18 + 48 + 5y  + 18 + 32 + 4y -8 + 42

= 9y + 150

Total Students = 2 + 8 + y + 6 + 4 + y-2 + 6

= 2y + 24

Mean = (9y + 150)/(2y + 24)

=> 5.5 = (9y + 150)/(2y + 24)

=> 11y + 132 = 9y + 150

=> 2y = 18

=> y = 9

Mode = 5  as max 9 students got these marks