Question

QUESTION 1 a) Consider the data of Table 1.1 which specifies the "life" of 40 similar car batteries recorded to the nearest tenth of a year. The batteries are guaranteed to last 3 years. Table 1.1 3.5 2.2 3.4 2.5 3.3 4.1 1.6 4.3 3.1 3.8 3.1 3.4 3.7 3.4 4.5 3.3 3.6 4.4 2.6 3.2 3.8 2.9 3.2 3.9 3.7 3.1 3.3 4.1 3.0 3.0 4.7 3.9 1.9 4.2 2.6 3.7 3.1 3.4 3.5 4.7 (i) Represent the above data in the stem and leaf. [3 marks) (ii) Determine the mean, mode, median and variance for the raw data. [11 marks] b) A psychologist administered a test of manual dexterity to 25 third-grade students. The times, in minutes, required to complete the test are given in Table 1.2. Table 1.2 4 5 7 4 6 8 9 7 8 5 8 9 8 7 10 9 10 7 5 8 8 11 8 7 9 (i) Construct a frequency distribution for the data in Table 1.2 containing class, class boundaries, frequency, cumulative frequency and midpoint. [8 marks] (ii) Sketch the histogram using cumulative frequency. [3 marks) [Total : 25 marks)

Answer 1

Solution i- a (i) stem and leaf plot stem leaf 9 2 2 s 66 9 3 0 0 1 J2 2 3 3 3 I 4 4 9 5 5 6 7 7 7 8 8 9 9 I 2 3 4 5 7 EX) mean = 136.7 40 3.427S - occurs mode 3.9 and 3.1 mode is the value which most in data... mode = 3.4 and 3.3 1.e. data is bimodal

median th observation + obs median = 7 ( 2 2 Ascending order of data, 1.6, 19, 212, 215, 216, 2:6, 29, 3, 3, 3.1, 3.1, 3.1, 3.1, 3.2, 3.2 3.3, 3.3, 3.3, 3.4, 3.4, 3.4, 3.4, 3.5, 3.5, 3.6 3.7 3.7 3.7 3.8, 38, 39, 3.9 4.1, 4.1, 4.2, 43, 44, 4.5, 9.7, 4.7. median I ( to obs. + ntt 2 obs. ) 1 2 2 (20th abs i 21th obs.) ₃ (3.4+3.4) median 3.9 variance Elx; 7) 2 n 19.2177 40 variance= 0.4804

Given, 4, 5, 7, 4, 6, 8, 9, 7, 8, 5, 8, 9, 8, 7, 10, 9, 10, 7, 5, 8, 8, 11, 8, 7,9 To find class width width l-s 1 + 1.322 x 10g, where, 1 = S - largest value in data smallest value in data sample size width 11 -4 1 + 1.3224 log,025 2.15 - width F class intervall midpoint frequency cf. 2 2 2-5 3.5 S-8 G.S 9.5 12.5 9 13 8-11 11-14 24 25

Histogram 30 25 cumulative frequency 15 5 5-8 Class interval