Question

3. Find the mean, median and mode of each of the following sets of data.
(i) 63, 72, 72, 85, 84
(ii) 7, 19, 19, 7, 25, 7
(iii) 18, 21, 18, 3, 12, 15, 18, 42, 6, 3, 24, 12
(iv) 7, 3, 4, 5, 2, 3, 4, 5, 7, 3, 4, 5, 7, 7, 5, 7, 3, 6, 7, 7​

Answer 1

Answer:

Step-by-step explanation:

(i) Mean = 63+72+72+85+84/5 = 376/5 = 75.2

Ascending Order = 63,72,72,84,85

Median = n =5(odd).

Median = 5+1/2 th term = 6/2 th term = 3rd Term = 72.

Mode = 72.

(ii) Mean = 7+19+19+7+25+7/5 =84/6= 14.

Ascending Order = 7,7,7,19,19,25

Median = 6(even).

Median = 7+19/2 = 26/2 = 13.

Mode = 7.

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Answer 2

Answer:

Recall the concepts:

Mean = $\frac{Sum\ of\ observations}{Total \ number \ of \ observations}$

Median is the middlemost value when the observations are arranged in ascending order

If the number of observations is odd, then the median is the middle value

If the number of observations is even, then the median is the average of two middle values

Mode is the most occurring value in the data

(i) 63, 72, 72, 85, 84

Sum of observations = 376

Total number of observations = 5

Mean = $\frac{376}{5}$ = 75.2

Ascending order = 63,72,72,84,85

Since the number of observations is 5,

Median = The third observation = 72

Mode = most occurring  observation = 72

(i) 63, 72, 72, 85, 84

Sum of observations = 376

Total number of observations = 5

Mean = $\frac{376}{5}$ = 75.2

Ascending order = 63,72,72,84,85

Since the number of observations is 5,

Median = The third observation = 72

Mode = most occurring  observation = 72

(ii) 7, 19, 19, 7, 25, 7

Sum of observations = 84

Total number of observations = 6

Mean = $\frac{84}{6}$ = 14

Ascending order = 7,7,7,19,19,25

Since the number of observations is 6

Median = The average of the two middle values = $\frac{7+19}{2}$ = 13

Mode = most occurring  observation = 7

(iii)  18, 21, 18, 3, 12, 15, 18, 42, 6, 3, 24, 12

Sum of observations = 192

Total number of observations = 12

Mean = $\frac{192}{12}$ = 16

Ascending order =3,3,6,12,12,15,18,18,18,21,24,42

Since the number of observations is 12,

Median = The average of the two middle values = $\frac{15+18}{2}$ = 16.5

Mode = most occurring  observation = 18

(iv) 7, 3, 4, 5, 2, 3, 4, 5, 7, 3, 4, 5, 7, 7, 5, 7, 3, 6, 7, 7​

Sum of observations = 101

Total number of observations = 20

Mean = $\frac{101}{20}$ = 5.05

Ascending order =2,3,3,3,3,4,4,4,5,5,5,5,6,7,7,7,7,7,7,7

Since the number of observations is 20,

Median = The average of the two middle values = $\frac{5+5}{2}$ = 5

Mode = most occurring  observation = 7

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