Interpreting Histograms Flashcards

All 7 cards in this deck

How do you read the frequency of a class from a histogram?

e.g. a bar of height $1.5$ over $10 < t \le 20$

Frequency density $\times$ class width (the area of the bar).

e.g. $1.5 \times 10 = 15$

How do you estimate the frequency in part of a class interval?

e.g. $150 < h \le 180$ has frequency $18$; estimate for $150 < h \le 160$

Assume the data is spread evenly and take that fraction of the class frequency.

e.g. $\frac{10}{30} \times 18 = 6$

In a histogram, what does one bar having a greater frequency density than another tell you?

That interval contains more values per unit of the quantity, so the data is more concentrated there.

What are the steps to estimate the fraction of the data in a given range from a histogram?

e.g. $150$ students in total; for $150 < h \le 170$ the whole bars have frequencies $30$, $51$ and $36$, and one third of a bar of frequency $18$ lies in the range

1. Add the frequencies of the whole bars in the range: $30 + 51 + 36 = 117$
2. Add the proportional part of any part-bar: $\frac{1}{3} \times 18 = 6$, giving $123$
3. Write this over the total frequency: $\frac{123}{150}$

True or false? To estimate the proportion of the data in a given range of a histogram, you divide the number of bars in that range by the total number of bars.

False. You divide the frequency (area) in the range by the total frequency (total area).

What are the steps to estimate a percentage of the data in part of a histogram?

e.g. over $50$ years the bars have frequency density $1.4$ for a width of $10$ and $0.7$ for a width of $30$; $20\%$ of these members are female

1. Find each frequency as area: $1.4 \times 10 = 14$ and $0.7 \times 30 = 21$
2. Add them: $14 + 21 = 35$ members over $50$
3. Take the percentage: $20\%$ of $35 = 7$ female members

What are the steps to estimate the value needed to be in the top $20\%$ of a histogram?

e.g. total frequency $60$; the highest bar covers scores $30$ to $40$ and has frequency $12$

1. Find the number needed: $20\%$ of $60 = 12$ people
2. Work down from the highest values, adding frequencies until you reach $12$: the $30$–$40$ bar alone gives $12$
3. Read off the value at that point: a score of $30$