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Find the mean by the step-deviation method with a = 146. The table gives the lifetimes (hours) of 40 lamps. Class 118–126: 3, 126–134: 5, 134–142: 9, 142–150: 12, 150–158: 5, 158–166: 4, 166–174: 2.

Class 10StatisticsStatistics and Probability
  • A145.78
  • B147.80
  • C146.00
  • D144.20

Step-by-Step Solution

Class marks 122, 130, 138, 146, 154, 162, 170 give u = −3, −2, −1, 0, 1, 2, 3. Σfu = −9 − 10 − 9 + 0 + 5 + 8 + 6 = −9 and Σf = 40. Mean = 146 + 8(−9/40) = 146 − 1.8 = 144.20 hours. (145.78 leaves out h = 8; 147.80 drops the minus sign.)
Answer: D) 144.20

Key idea: Median for grouped data

**Step 1**: build cumulative frequency (cf) column.
**Step 2**: find n/2 (half the total frequency).
**Step 3**: locate the **median class** — the FIRST class whose cumulative frequency ≥ n/2.
**Step 4**: Apply formula.

**Median formula**:
**Median = l + h × (n/2 − cf) / f**

Where:
- l = lower limit of median class
- h = class width
- n = total frequency
- cf = cumulative frequency of class BEFORE median class
- f = frequency of median class

The formula uses linear interpolation within the median class to find where the n/2-th item falls.

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