Central Tendency: Exercise.

  1. Find the mean, median, and mode of the following data sets.
    1. 5.50, 6.50, 5.55, 7.75, 5.55
    2. 4, 5, 5, 4, 6, 7, 5, 5
    3. 70, 85, 89, 81, 96, 85, 85, 92, 96

  2. The bar chart below shows the number of children in a selection of families in Springfield Town.
    1. How many families are in this survey?
    2. Write down the mode.
    3. Estimate the median of this distribution.
    4. Estimate the mean number of children in a family.

  3. The histogram shows the weight gain in a group of student after arriving at a boarding school.
    1. Find the mode.
    2. Find the mean.
    3. Find the median.

  4. A group of students are asked how many emails do they write in a day. The results are summarised in the frequency distribution table below.
    Number of letters, x Number of students, f xf
    0 3  
    1 8  
    2 12  
    3 15  
    1. Complete the above table.
    2. What is the modal number of letters written?
    3. Find the mean number of letters written.
    4. Find the median number of letters written.

  5. Amy recorded the number of words in each title of CD collection. The results are shown in the frequency distribution table.
    Class interval
    (number of words)
    Frequency, f
    1-10 10
    11-20 12
    21-30 2
    31-40 1
    1. Find the class interval in which the median lies.
    2. Estimate the mean number of words in a CD title to the nearest whole number.

  6. The following table shows the age distibution of teachers who play tennis at Springfield High School.
    Ages Frequency Mid-interval values
    20 ≤ x < 30 2  
    30 ≤ x < 40 8  
    40 ≤ x < 50 5  
    50 ≤ x < 60 3  
    1. Complete the above table.
    2. Which is the modal group in the above distribution?
    3. The median lies in which group?
    4. Estimate the mean in this distribution.

  7. The table shows the scores of a group of students in a trivial-quiz competition.
    score
    100
    200
    300
    400
    500
    Frequency
    3
    2
    k
    5
    1
    The mean score is 295. Find the value k.
  8. There were 6 people in the lift with the mean weight being 60 kg. A child with a weight of x kg got out from the lift on the 5th floor. A lady whose weight was y kg walked into the lift on the 5th floor. What is the mean weight now if the lady is 40 kg heavier than the child?

Solutions