Each value with how often it occurs: A frequency table lists each data value (or class) with its frequency — how many times it occurs.
Add a column of frequencies to get the total; the mode is the value with the highest frequency.
A histogram groups data into equal class intervals; bar heights are the frequencies (bars touch). The tallest bar is the modal class.
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IB-style question — read the table
A survey of 40 households records the number of pets owned: 0 pets → 9 households, 1 → 15, 2 → 11, 3 → 5.
Find the mode and the number of households with at least 2 pets.
Step by step
- Mode = the value with the highest frequency.
- 'At least 2' means 2 or 3.
Final answer
Mode = 1 pet; 16 households own at least 2 pets.
Mode = most frequent VALUE: The mode is the data value, not its frequency — here the mode is 1, not 15.
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Bars for grouped continuous data: A histogram shows grouped continuous data.
With equal-width classes the bar height is the frequency, and the bars touch (no gaps).
Add the heights to get the total.
IB-style question — read a histogram
A histogram of parcel masses uses equal 2 kg classes with frequencies 6, 14, 18, 9, 3.
Find the total number of parcels and how many weigh under 4 kg.
Step by step
- Total = sum of all the bar heights.
- 'Under 4 kg' = first two classes.
Final answer
50 parcels in total; 20 weigh under 4 kg.
Continuous data → bars touch: Histograms are for continuous data, so the bars touch.
Bar charts (gaps between bars) are for categories — don't confuse them.
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The tallest bar's class: For grouped data the modal class is the class with the greatest frequency (the tallest bar).
You can also describe the shape: roughly symmetric, or skewed toward higher/lower values.
IB-style question — modal class
Heights (cm) are grouped: 150–160 → 5, 160–170 → 12, 170–180 → 9, 180–190 → 4.
State the modal class and describe the distribution.
Step by step
- Modal class = the class with the highest frequency.
- Compare the tails.
Final answer
Modal class 160 ≤ h < 170 cm; the distribution rises to that class then falls away (roughly symmetric).
Modal class ≠ a single mode: For grouped data you can only name the modal class (an interval), not a single modal value.