Theory question 114
StatisticsThe distribution of the lives (in days) of 40 transistor batteries is shown in the table.
Battery life (in days): 26-30, 31-35, 36-40, 41-45, 46-50, 51-55
Frequency: 4, 7, 13, 8, 6, 2
(a) Draw a histogram for the distribution (b) Use your graph in (a) to determine the mode for the distribution. (c) Using an assumed mean of 43 days, calculate the mean of the distribution. (d) What percentage number of batteries will live for less than 31 days or more than 45 days?
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(a) Bars on class boundaries 25.5, 30.5, …, 55.5 with heights 4, 7, 13, 8, 6, 2
(b) Modal class 35.5–40.5; crossing lines give mode ≈ 35.5 + 6/(6 + 5) × 5 ≈ 38.2 days
(c) Mid-points 28, 33, 38, 43, 48, 53; d = −15, −10, −5, 0, 5, 10; Σfd = −145
Mean = 43 − 145/40 = 39.375 ≈ 39.4 days
(d) Less than 31: 4; more than 45: 6 + 2 = 8; 12/40 × 100 = 30%
On the histogram, join the corners of the tallest bar to the neighbouring bars; their crossing gives the mode.