Question

1)The scores in the math test (out of 25) of 15 students is as follows:
19,25,23,20,9,20,15,10,5,16,25,20,24,12,20.
Find the mode and median of this data.Are they same?

2)The weights (in​​​​​ kg) of 15 students of class are :
38,42,35,37,45,50,32,43,43,40,36,38,43,38,47.
Find the median and mode of this data.Is there more than one mode?

Answer 1

(1)
Scores of 15 students in mathematics test are: 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 Arranging these scores in an ascending order, 5, 9, 10, 12, 15, 16, 19, 20 ,20 ,20 , 20, 23, 24, 25, 25 Mode of a given data is that value of observation which occurs for the most numbers of times. Median of a given data is the middle observation when the data is arranged in an ascending order. As there are 15 terms in the given data, therefore the median of this data will be the 8th observation((15+1)/2=8). Hence, median = 20 Also, it can be observed that 20 occurs 4 times (i.e., maximum number of times). Therefore, mode of this data = 20 Yes, both are same.
2)The weights (in​​​​​ kg) of 15 students of class are :
38,42,35,37,45,50,32,43,43,40,36,38,43,38,47.

The weights can be arranged in ascending order as follows: (32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50)

Weight (in kg) Tally marks No. of students

32	|	1
35	|	1
36	|	1
37	|	1
38	|||	3
40	|	1
42	|	1
43	|||	3
45	|	1
47	|	1
50	|	1
Total		15

Mode = 38 and 43
Median = 40 (Eighth observation)((15+1)/2=8)
There are two modes(38 and 43) in this data.