Measures of central tendency flashcards

Topic 4: Measures of central tendency

How do you find the mean from a list and from a frequency table?

List: mean = Σx ÷ n. Frequency table: mean = Σfx ÷ Σf. Divide by Σf, never by the number of rows.

How do you find the median of a list?

Put the values in order; the median is at position (n + 1)/2. For even n, take the mean of the two middle values. Example: 3, 4, 6, 8, 9, 12 → (6 + 8) ÷ 2 = 7.

What is the mode of a frequency table?

The value x with the largest frequency. Quote the value, not the frequency. A data set can have no mode or more than one.

How do you estimate the mean of a grouped frequency distribution?

Use each class midpoint as x: mean ≈ Σfx ÷ Σf. Example: 0–10, 10–20, 20–30 with frequencies 3, 5, 2 → (15 + 75 + 50) ÷ 10 = 14. Say it is an estimate.

How do you estimate the median of grouped data by interpolation?

Median ≈ lower boundary + (n/2 − cf before the class) ÷ f(class) × class width. Example: n = 40, class 30 to under 40 has f = 12, 12 values below 30 → 30 + 8/12 × 10 = 36.7.

How do you find the modal class when class widths are unequal?

Choose the class with the highest frequency density (frequency ÷ width), not the highest frequency. Example: 0–10 (8), 10–20 (12), 20–40 (20) → densities 0.8, 1.2, 1.0, so the modal class is 10 to under 20.

How do you find a missing value when the mean is given?

Total = mean × number of values. Example: five values have mean 12, so the total is 60. If four of them add to 47, the fifth is 13.

How do you find the combined mean of two groups?

(total of A + total of B) ÷ (number in A + number in B). Never average the two means unless the groups are the same size.

When is the median a better average than the mean?

When the data is skewed or has an extreme value. One very high pay figure inflates the mean, but the median is unaffected.

When is the mode the most suitable average?

When you need the most common item or category, such as which dish a canteen should prepare most of. It is the only average that works for categorical data.

Why should you avoid estimating the mean when the last class is "60 and over"?

An open-ended class has no upper boundary, so it has no midpoint to use in Σfx.

Why are a grouped mean and a grouped median only estimates?

The individual values in each class are unknown. The mean assumes they sit at the midpoint, and the median assumes they are spread evenly through the class.