Representation of Data Questions and Answers - Form 2 Topical Mathematics

Questions

1. Below is a histogram, draw.
   
   Use the histogram above to complete the frequency table below:
   
2. Wambui spent her salary as follows:
   
   
   Draw a pie chart to represent the above information
3. The examination marks in a mathematics test for 60 students were as follows;-
   
   From the table;
   1. State the modal class
   2. On the grid provided, draw a histogram to represent the above information
4. The marks scored by 200 from 4 students of a school were recorded as in the table below.
   
   
   1. On the graph paper provided, draw a histogram to represent this information.
   2. On the same diagram, construct a frequency polygon.
   3. Use your histogram to estimate the modal mark.
5. The diagram below shows a histogram representing the marks obtained in a certain test:-
   
   
   1. If the frequency of the first class is 20, prepare a frequency distribution table for the data
   2. State the modal class
   3. Estimate:
      1. The mean mark
      2. The median mark
6. The data below shows the number of sessions different subjects are taught in a week. Draw a pie chart to show the data:
   
7. The heights of 50 athletes in Moi University team were shown below:
   
   
   1. State the modal class
   2. Calculate the median height of the athletes
8. The table below shows the length of 40 mango tree leaves;
   
   
   1. Determine the;
      1. Modal class
      2. Median class
   2. Calculate;
      1. The mean of the leaves
      2. The median of the leaves

Answers

1. 
   
2. Food: ⁴⁰/₁₀₀ x 360 = 144^°
   Transport: ¹⁰/₁₀₀ x 360 = 36^°
   Education: ²⁰/₁₀₀ x 360 = 72^°
   Clothing: ²⁰/₁₀₀ x 360 = 72^°
   Rent: ¹⁰/₁₀₀ x 360 = 36^°
3. 1. 
      
   2. 
      
4. For correct class boundaries
   For correct class intervals.
   All frequency densities
   Correct scale
   All the bars drawn.
   Top mid pts. Of bars indicated.
   For the mid pts. Joint to make a polygon.
   For correctly identifying the modal mark point.
   For reading correctly the modal mark ≡ 53.5 ± 0.1
5. 1. 
      
   2. Modal class is 10-19
   3. 1. Class
         
         x= ^∑fx/_∑f = ³³⁸⁰/₁₄₀ = 24.14
      2. Median mark is at 70 + 71 = 70.5^th position
         Median = 119.5 + ^(0.5)/₄₀ x 20
         = 19.5 + 0.25
         = 19.75
6. Total No. of sessions
   = 8 + 7 + 4 + 3 = 22
   Angle for:
   English = ⁸/₂₂ x 360 = 130.9^°
   Maths = ⁷/₂₂ x 360 = 114.5^°
   Chemistry = ⁴/₂₂ x 360 = 65.5^°
   CRE = ³/₂₂ x 360 = 49.01^° 
   
7. 180 – 189
             Class limits
   
   Median = ⁵⁰/₂ = 25
   179.5 + ^(25–23)/₁₆ x 10
   = 179.5 + ²⁰/₁₆ = 180.75
   179.5 + ^(26–23)/₁₆ x 10
   179.5 + ³⁰/₁₆ = 181.38
   ^{(180.75 + 181.38)}/2
   = 181.06
8. 1. 1. 145 – 153
      2. Median class
         (40 + ½)^th value  » median class = 145 – 153
         This is the 20.5^th value
         The value also in the 145 – 153 class
   2. 
      
      B2 for all values of fx correct and B1 for 4 values of fx and above orrect
      Mean = ^Efx/_Ef = ⁵⁸⁸⁸/₄₀ = 147.2mm
      Median 20th = 144.5 + (11/12 x 9) = 152.75
      21^st = 144.5 + (¹²/₁₂ x 9) = 153.5
      Median = ^{(152.75 + 153.5)}/₂ = 153.125
      (Alternatively, one could work out the 20.5 value directly using median formula)