STA301 Assignment No 1 spring fall 25 October 2011

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Class Boundaries f 19.5-29.5 5 29.5-39.5 4 39.5-49.5 5 49.5-59.5 8 59.5-69.5 12 59.5-79.5 16 total 50 Solution of sta301 1st assignment for idea by Muhammad Adnan (b) How many men fall in the age of 50 or above? Men above 50 = 8+12+16=36 (c) men fall between the age group of 60 and 69= =12 (ii) Write down the following figure in the form of frequency table and also find the relative frequency. Class Boundaries f Relative frequncy 19.5-29.5 5 5/50=0.1 29.5-39.5 4 4/50=0.08 39.5-49.5 5 5/50=0.1 49.5-59.5 8 8/50= 59.5-69.5 12 12/5= 59.5-79.5 16 16/50= total 50 Question 2:Marks: 5+5=10 (i) Calculate the mode from the following continuous distribution. Height Number (f) 57.5-60.0 6 60.0-62.5 26 62.5-65.0 190 65.0-67.5 281----f1 l--67.5-70.0 412---model class 70.0-72.5 127-----f2 72.5-75.0 38 Total 1080 Ans= Mode = l + fm-f1/(fm-f1)+(fm-f2) * h Fm = frequency of model class = highest frequency =412 H= difference between class boundries = 2.5 So… Mode= 67.5+412-281/(412-281)+(412-127)*2.5 = 67.5+131/(131)+(285)*2.5 = 68.287 (ii). Use the stem and leaf plot to answer these questions. Statistics Test Scores Stem Leaf 6 1 1 4 6 7 8 7 2 3 5 7 9 8 1 3 5 6 6 7 7 8 9 9 0 0 3 4 6 8 9 9 10 0 0 a) What is the best test score? Ans best score 100 b) How many students take the test? Ans 30students c) How many students scored 90? Ans 02students made 90 d) What is the lowest score? Ans lowest score= 61 e) Find the difference between the high and low scores. Ans high score = 100 Lowest = 61 Difference = 100- 61 =59 Question 3:Marks: 3+3+4=10(i) Find the median for the following discrete frequency distribution.Number of pupils per class Number of Classes F cf 20 1 1 21 0 1 22 1 2 23 3 5 24 6 11 25 9 20 26 8 28 27 10 38 28 7 45 Total 45 Median=n+1/2 for more detail page no61 of HO 45+1/2 median =23rd value is lying in 26the distribution so median = 26 (ii) Calculate the weighted mean from the following dataItem Expenditure Weights Food 290 7.5 Rent 54 2.0 Clothing 98 1.5 Fuel and light 75 1.0 solve from page no58 of HO Other items 75 0.5 (iii) A man gets a rise of 10% in salary at the end of his first year of service and further of 20 % and 25 % at the end of the second and third year respectively. The rise in each case is calculated on his salary at the beginning of the year. To what annual percentage increase is this equivalent? Ans Annual percentage increase in his salary = 10%+20%+25%/3 = 55/3 = 18.33%