Question

Chebyshev’s Theorem

For any set of data:
At least 75% of the data fall in the interval from __________ to __________. At least 88.9% of the data fall in the interval from __________ to __________. At least 93.8% of the data fall in the interval from __________ to __________.

Answer 1

Explanation:

At least 75% of the data fall in the interval from the first quartile (Q1) to the third quartile (Q3).

At least 88.9% of the data fall in the interval from the first decile (D1) to the ninth decile (D9).

At least 93.8% of the data fall in the interval from the second percentile (P2) to the 98th percentile (P98).

Note: The quartiles, deciles, and percentiles divide a set of data into 100 equal parts and provide information about the distribution of the data. The first quartile (Q1) is the 25th percentile, the third quartile (Q3) is the 75th percentile, the first decile (D1) is the 10th percentile, the ninth decile (D9) is the 90th percentile, the second percentile (P2) is the 2nd percentile, and the 98th percentile (P98) is the 98th percentile.