Mathematics
At a shooting competition the scores of a competitor were as given below :
Score | No. of shots |
---|---|
0 | 0 |
1 | 3 |
2 | 6 |
3 | 4 |
4 | 7 |
5 | 5 |
(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 frequency | fx |
---|---|---|---|
0 | 0 | 0 | 0 |
1 | 3 | 3 (0 + 3) | 3 |
2 | 6 | 9 (3 + 6) | 12 |
3 | 4 | 13 (9 + 4) | 12 |
4 | 7 | 20 (13 + 7) | 28 |
5 | 5 | 25 (20 + 5) | 25 |
Total | 25 | 80 |
Here, n = 25, which is odd.
By formula,
Median = th term = = 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 = = 3.2
Hence, mean = 3.2
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Related Questions
The following table shows the expenditure of 60 boys on books. Find the mode of their expenditure.
Expenditure (₹) No. of students 20 - 25 4 25 - 30 7 30 - 35 23 35 - 40 18 40 - 45 6 45 - 50 2 A boy scored the following marks in various class tests during a term, each test being marked out of 20.
15, 17, 16, 7, 10, 12, 14, 16, 19, 12 and 16.
(i) What are his modal marks ?
(ii) What are his median marks ?
(iii) What are his total marks ?
(iv) What are his mean marks ?
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(2 + 40)
840
The median of 10, 12, 9, 8, 12, 13, 8, 15 and 12 is :
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13