Interpreting Cumulative Frequency Diagrams Flashcards

All 8 cards in this deck

How do you estimate the median from a cumulative frequency graph?
e.g. a graph for $60$ students

Read across from cumulative frequency $\frac{n}{2}=30$ to the curve, then down to the horizontal axis.

At which cumulative frequencies do you read off the lower and upper quartiles?
e.g. a graph for $60$ students

Lower quartile at $\frac{n}{4}=15$ and upper quartile at $\frac{3n}{4}=45$; read across to the curve then down.

How do you estimate the number of values greater than a given value from a cumulative frequency graph?
e.g. of $60$ students, how many are taller than $160$ cm

Read the cumulative frequency at that value and subtract it from the total: if the reading at $160$ is $48$, the answer is $60-48=12$.

How do you estimate the number of values between two given values from a cumulative frequency graph?
e.g. between $40$ g and $60$ g

Read the cumulative frequency at each value and subtract: if the readings are $20$ at $40$ g and $50$ at $60$ g, the answer is $50-20=30$.

How do you estimate the 90th percentile from a cumulative frequency graph?
e.g. a graph for $80$ items

Read across at $90\%$ of the total, $0.9\times80=72$, then down to the horizontal axis.

How do you check a claim about the median using a cumulative frequency graph?

Read the median from the graph and compare it with the claimed value.
e.g. for $60$ potatoes, read across at $30$: the median is $57$ g, so the claim that it is $50$ g is wrong.

True or false? The median and quartiles found from a cumulative frequency graph are only estimates.

True. The original data is grouped, so exact values are unknown and readings from the curve are estimates.

How do you estimate what percentage of the data is below a given value on a cumulative frequency graph?

e.g. the percentage of 80 plants shorter than 90 cm

Read the cumulative frequency at that value, then divide by the total and multiply by 100.
e.g. reading 74 gives $\frac{74}{80}\times100=92.5\%$