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Question 1

Heights (cm) of plants under treatment A (80 samples):

\begin{array}{|c|c|} \hline \text{Height (cm)} & f \\ \hline 10\text{--}19 & 5 \\ 20\text{--}29 & 15 \\ 30\text{--}39 & 30 \\ 40\text{--}49 & 20 \\ 50\text{--}59 & 10 \\ \hline \end{array}

Find the mean, median, modal class and range.

[7]

Question 2

The distribution of lifespans (in years) of a species is:

\begin{array}{c c} \text{Lifespan} & f \\ 2\text{--}4 & 3 \\ 5\text{--}7 & 7 \\ 8\text{--}10 & 15 \\ 11\text{--}13 & 10 \\ 14\text{--}16 & 5 \end{array}

Find the mean, median, modal class and range.

[7]

Question 3

Weekly incomes (in £) for 60 households are tabulated:

\begin{array}{|c|c|} \hline \text{Income (£)} & f \\ \hline 200\text{--}299 & 5 \\ 300\text{--}399 & 12 \\ 400\text{--}499 & 25 \\ 500\text{--}599 & 10 \\ 600\text{--}699 & 8 \\ \hline \end{array}

Calculate the mean, median, modal class and range.

[9]

Question 4

A research study records cholesterol levels (mg/dL) for 50 subjects:

\begin{array}{c c} \text{Cholesterol} & f \\ 150\text{--}169 & 7 \\ 170\text{--}189 & 15 \\ 190\text{--}209 & 18 \\ 210\text{--}229 & 6 \\ 230\text{--}249 & 4 \end{array}

Estimate the mean and median. Determine the modal class and the range.

[8]

Question 5

Given the following frequency distribution of exam scores, calculate the mean, median, modal class and range of the data:

\begin{array}{c c} \text{Score } (x) & f \\ 10\text{--}19 & 2 \\ 20\text{--}29 & 5 \\ 30\text{--}39 & 8 \\ 40\text{--}49 & 4 \\ 50\text{--}59 & 1 \end{array}

[9]

Question 6

The daily rainfall (in mm) over $30$ days is shown in the following table:

\begin{array}{|c|c|} \hline \text{Rainfall (mm)} & f \\ \hline 0\text{--}4 & 8 \\ 5\text{--}9 & 10 \\ 10\text{--}14 & 6 \\ 15\text{--}19 & 4 \\ 20\text{--}24 & 2 \\ \hline \end{array}

Find the mean, median, modal class and range.

[7]

Question 7

The distribution of daily caloric intake (kcal) for 100 individuals is shown in the table below:

\begin{array}{|c|c|} \hline \text{Intake (kcal)} & f \\ \hline 1200\text{--}1399 & 8 \\ 1400\text{--}1599 & 22 \\ 1600\text{--}1799 & 30 \\ 1800\text{--}1999 & 25 \\ 2000\text{--}2199 & 10 \\ 2200\text{--}2399 & 5 \\ \hline \end{array}

1.

(a) State the modal class.

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2.

(b) Calculate an estimate of the mean daily caloric intake.

[3]

3.

(c) Calculate an estimate of the median daily caloric intake.

[3]

4.

(d) Determine the range of the daily caloric intake.

[2]

Question 8

A factory records daily production in batches over 30 days as follows. Find the mean, median, modal class and range:

\begin{array}{|c|c|} \hline \text{Batches per day} & f \\ \hline 100\text{--}119 & 4 \\ 120\text{--}139 & 10 \\ 140\text{--}159 & 8 \\ 160\text{--}179 & 6 \\ 180\text{--}199 & 2 \\ \hline \end{array}

[8]

Question 9

Speeds (km/h) of 45 vehicles passing a checkpoint are recorded in the table below:

\begin{array}{|c|c|} \hline \text{Speed (km/h)} & \text{Frequency} \\ \hline 40\text{--}49 & 5 \\ \hline 50\text{--}59 & 15 \\ \hline 60\text{--}69 & 18 \\ \hline 70\text{--}79 & 6 \\ \hline 80\text{--}89 & 1 \\ \hline \end{array}

Calculate the mean, median, modal class, and range.

[6]

Question 10

A survey of weekly study hours for 40 students yields:

\begin{array}{c c} \text{Hours} & f \\ 0\text{--}9 & 6 \\ 10\text{--}19 & 14 \\ 20\text{--}29 & 12 \\ 30\text{--}39 & 5 \\ 40\text{--}49 & 3 \end{array}

Calculate the mean, median, modal class and range.

[6]

Question 11

The ages of participants in a marathon are grouped as follows. Determine the mean, median, modal class and range:

\begin{array}{c c} \text{Age (years)} & f \\ 18\text{--}24 & 5 \\ 25\text{--}31 & 12 \\ 32\text{--}38 & 9 \\ 39\text{--}45 & 4 \\ 46\text{--}52 & 0 \\ 53\text{--}59 & 2 \end{array}

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Question Type 3: Given a frequency table, calculating the mean, median, modal class and range of the data Exercises