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Descriptive statisticsStatistics and probabilityMiddle schoolabout 1:09

Mean, median, mode of 8, 16, 23, 16, 5, 20: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: Mean = 14.66666667; Median = 16; Mode = 16; Range = 18.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.5 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Mean, median and mode
Data: 8, 16, 23, 16, 5, 20
2. Steps, part 1
1. $5, 8, 16, 16, 20, 23\quad (n = 6)$
  Sort the data from smallest to largest
2. $\bar{x} = \frac{88}{6} = 14.66666667$
  Mean: add the values and divide by how many there are
3. $\text{median} = \frac{16 + 16}{2} = 16$
  Median: the middle value of the sorted list
4. Mode: the value(s) that appear most often
3. Steps, part 2
1. $23 - 5 = 18$
  Range: largest minus smallest
4. The answer
$\text{Mean = 14.66666667; Median = 16; Mode = 16; Range = 18}$
mean 14.66666667, median 16, mode 16, range 18
5. Check
- Sum 88 = mean × n = 14.66666667 × 6 = 88

Transcript

The problem. Here is the problem: Data: 8, 16, 23, 16, 5, 20. Measures of central tendency for a list of numbers.

Steps, part 1. Sort the data from smallest to largest. Mean: add the values and divide by how many there are. Median: the middle value of the sorted list. With 6 values (even), the median is the average of values 3 and 4. Mode: the value(s) that appear most often. Most frequent: 16.

Steps, part 2. Range: largest minus smallest.

The answer. So the answer is Mean equals 14.66666667; Median equals 16; Mode equals 16; Range equals 18. The mean balances all values, the median splits the sorted data in half and is less affected by outliers, and the mode is the most common value.

Check. Sum 88 equals mean times n equals 14.66666667 times 6 equals 88.

About descriptive statistics

Mean, median, mode, range, variance and standard deviation of a data set.

Mean, median, mode of 8, 16, 23, 16, 5, 20: Animated Lesson