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Mathematics

At a shooting competition the scores of a competitor were as given below :

ScoreNo. of shots
00
13
26
34
47
55

(i) What was his modal score ?

(ii) What was his median score ?

(iii) What was his total score ?

(iv) What was his mean score ?

Measures of Central Tendency

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Answer

(i) From above table,

The score 4 has the maximum frequency.

Hence, modal score = 4.

(ii) Cumulative frequency distribution table :

Score (x)No. of shots (f)Cumulative frequencyfx
0000
133 (0 + 3)3
269 (3 + 6)12
3413 (9 + 4)12
4720 (13 + 7)28
5525 (20 + 5)25
Total2580

Here, n = 25, which is odd.

By formula,

Median = n+12\dfrac{n + 1}{2} th term = 25+12=262\dfrac{25 + 1}{2} = \dfrac{26}{2} = 13th term

From table, score of 10th to 13th term is 3.

Hence, median = 3.

(iii) From cumulative frequency distribution table we get,

Total score = 80.

Hence, total score = 80.

(iv) By formula,

Mean = ΣfxΣf=8025\dfrac{Σfx}{Σf} = \dfrac{80}{25} = 3.2

Hence, mean = 3.2

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