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Zorluk: OrtaMeasures of Central Tendency

Review the four distinct practical situations below. Pair each descriptive problem with its mathematically correct calculated result.

  • A baker used 44, 88, 1111, and 1313 cups of sugar over four days. Determine the mean daily usage.99
  • A delivery driver logged 55, 1212, 77, 1414, 99, and 1111 miles on six different routes. Find the median distance.1010
  • A retail shop sold hats in sizes 88, 66, 88, 1212, 66, 88, and 1515. Identify the mode.88
  • A student earned scores of 66 and 1010 on two assignments. Find the score needed on the third assignment to achieve a mean of 99.1111

Cevap

The correct matches are: Mean usage is 99, median distance is 1010, mode size is 88, and the required assignment score is 1111.
Each statistical measure is calculated according to its definition: the mean is the sum divided by the count, the median is the middle value of an ordered list (or average of two middle values), the mode is the most frequent value, and a missing value can be found algebraically using the mean formula.

Adım Adım Çözüm

1
Determine the mean for the baker's sugar usage.
The sum is 3636, divided by 44 equals 99.
The arithmetic mean requires dividing the sum of all values by the total count of values.
2
Determine the median for the delivery driver's distances.
The sorted list is 5,7,9,11,12,145, 7, 9, 11, 12, 14. The average of the middle two values is (9+11)÷2=10(9 + 11) \div 2 = 10.
For an even number of data points, the median is the average of the two middle numbers in an ordered list.
3
Determine the mode for the hat sizes.
The mode is 88.
The mode is the value that appears most often in a dataset.
4
Calculate the missing assignment score.
The required score is 1111.
Using the algebraic formula for mean: (6+10+x)÷3=9(6 + 10 + x) \div 3 = 9, which simplifies to 16+x=2716 + x = 27.

Anahtar Kavram

Measures of central tendency (mean, median, mode) and using algebraic substitution to find a missing data point given a target mean.
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Konular

Measures of Central Tendency

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