Exercise Set 18

  1. The following table contains students’ exam marks.

    75 85 59 73 88 65 60 86 72 63 78 61 75 78 74 67
    60 68 74 66 82 78 94 73 71 83 79 96 67 62 75 81
    75 71 65 79 73 80 78 72 74 53 76 65 73 67 72 63
    1. Create a frequency distribution table with classes 50-59, 60-69,… etc.
    2. Draw a histogram from the table.

  2. The following table shows the results of 178 measurements of the carbon content of a mixed powder fed to a plant over a period of one month.

    Range of values of Carbon (%) Frequency
    4.10-4.19 1
    4.20-4.29 2
    4.30-4.39 7
    4.40-4.49 20
    4.50-4.59 24
    4.60-4.69 31
    4.70-4.79 38
    4.80-4.89 24
    4.90-4.99 21
    5.00-5.09 7
    5.10-5.19 3
    Total 178

    From this frequency distribution, construct:

    1. a histogram
    2. a frequency polygon
    3. an ogive

    From the ogive, estimate the percentage of measurements showing a carbon content below 5.00%.

  3. The following numbers are the marks obtained by 50 students in an examination:

    57 60 37 74 62 40 56 59 80 60
    62 94 78 73 56 68 67 79 83 87
    90 93 58 46 77 63 66 66 56 71
    51 77 53 69 70 69 70 70 47 54
    49 54 68 35 64 67 76 73 68 61
    1. Reduce these marks to a frequency distribution, with equal class widths, having as the first interval 35-44 inclusive. Draw an ogive for the distribution.
    2. Using the graph, what is the median mark?
    3. Use your graph to estimate what % of students pass the examination if the pass mark is 55.

  4. A sample of underweight babies was fed a special diet and the following weight gains (lbs) were observed at the end of three months: 6.7, 2.7, 2.5, 3.6, 3.4, 4.1, 4.8, 5.9, 8.3. What are the mean and standard deviation?

  5. In an examination, the marks awarded to the first 40 scripts were:

    32, 57, 43, 65, 28, 60, 47, 52, 39, 48, 25, 53, 47, 52, 62, 31, 38, 46, 72, 51, 29, 45, 54, 48, 50, 66, 63, 36, 23, 43, 32, 39, 58, 55, 29, 48, 37, 43, 54, 40.

    1. Taking classes 14.5-24.5, 24.5-34.5, 34.5-44.5 etc, draw up a frequency distribution table for the marks. Also estimate the relative frequency, cumulative frequency and relative cumulative frequency.
    2. Draw a histogram, frequency polygon and ogive for this frequency distribution.
    3. From the frequency table, estimate the mean, variance and standard deviation of the marks.

  6. A city has been criticized for its excessive discharges of untreated sewage into the nearby river. A microbiologist take 45 samples of water downstream from the treated sewage outlet and measures the number of bacteria present. A summary table is as follows:

    Number of Bacteria Number of Samples
    20-30 5
    30-40 20
    40-50 15
    50-60 5

    What are the \(25^{\text{th}}\) and \(75^{\text{th}}\) percentiles?