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Math  /  Data & Statistics

QuestionThe table shows some information about the profit made each day at a cricket club on 100 days. (a) Complete the cumulative frequency table. \begin{tabular}{|c|c|} \hline Pront (£x) & \begin{tabular}{c} Crmulative \\ frequency \end{tabular} \\ \hline 0≤x<500 \leq x<50 & \\ \hline 0≤x<1000 \leq x<100 & \\ \hline 0≤x<1500 \leq x<150 & \\ \hline 0≤x<2000 \leq x<200 & \\ \hline 0≤x<2500 \leq x<250 & \\ \hline 0≤x<3000 \leq x<300 & \\ \hline \end{tabular} (b) On the grid, draw a cumulative frequency graph for this information. \begin{tabular}{|c|c|} \hline Proft ( £x)£ x) & Frequency \\ \hline 0≤x<500 \leq x<50 & 10 \\ \hline 50≤x<10050 \leq x<100 & 15 \\ \hline 100≤x<150100 \leq x<150 & 25 \\ \hline 150≤x<200150 \leq x<200 & 30 \\ \hline 200≤x<250200 \leq x<250 & 5 \\ \hline 250≤x<300250 \leq x<300 & 15 \\ \hline \end{tabular} (1) (2) (c) Use your graph to find an estimate for the number of days on which the profit was less than £125£ 125 days \qquad (d) Use your graph to find an estimate for the interquartile range.

Studdy Solution

STEP 1

1. The cumulative frequency is the running total of frequencies up to the upper boundary of each class interval.
2. The cumulative frequency graph is plotted with the upper boundary of each class interval on the x-axis and the cumulative frequency on the y-axis.
3. The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1).

STEP 2

1. Complete the cumulative frequency table.
2. Draw the cumulative frequency graph.
3. Estimate the number of days with profit less than £125.
4. Estimate the interquartile range.

STEP 3

Calculate the cumulative frequency for each class interval:
- 0≤x<500 \leq x < 50: Cumulative frequency = 10 - 0≤x<1000 \leq x < 100: Cumulative frequency = 10 + 15 = 25 - 0≤x<1500 \leq x < 150: Cumulative frequency = 25 + 25 = 50 - 0≤x<2000 \leq x < 200: Cumulative frequency = 50 + 30 = 80 - 0≤x<2500 \leq x < 250: Cumulative frequency = 80 + 5 = 85 - 0≤x<3000 \leq x < 300: Cumulative frequency = 85 + 15 = 100

STEP 4

Plot the cumulative frequency graph:
- Plot points at (50, 10), (100, 25), (150, 50), (200, 80), (250, 85), (300, 100). - Connect the points with a smooth curve.

STEP 5

Estimate the number of days with profit less than £125:
- Locate £125 on the x-axis. - Find the corresponding cumulative frequency on the y-axis. - Estimate the number of days.

STEP 6

Estimate the interquartile range:
- Find Q1 (25th percentile) and Q3 (75th percentile) from the graph. - Subtract Q1 from Q3 to find the interquartile range.
The cumulative frequency table is completed, and the graph is drawn. Use the graph to estimate the number of days with profit less than £125 and the interquartile range.

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