The amount that two groups of students spent on snacks in one day is shown in the dot plots below.
Group A
A dot plot titled Group A. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Group B
A dot plot titled Group B. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 3 above 1, 2 above 2, 4 above 3, 0 above 4, and 1 above 5.
Which statements about the measures of center are true? Select three choices.
The mean for Group A is less than the mean for Group B.
The median for Group A is less than the median for Group B.
The mode for Group A is less than the mode for Group B.
The median for Group A is 2.
The median for Group B is 3.
Answers
Answer:
Answer:
Below is proved that for the set of data described none measure for group B is $1 greater than for group A.
Explanation:
The information for the two groups may be summarized in this way.
Note that each dot is one student, and that here I use * to represent the dots.
Group A:
$0: __ (0 dots)
$1: * * * * * (5 dots)
$2: * * * * (4 dots)
$3: * (1 dot)
$4: __ (0 dots)
$5: __ (0 dots)
Total number of dots: 5 + 4 + 1 = 10
Mode: $1 (the value that is repeated more times, 5 times).
Mean: [$1 × 5 + $2 × 4 + $3 × 1 ] / 10 = $11 / 10 = $1.1
Median: [the value of the sixth point - value of the fifth point ] / 2 = [$1 + $2] / 2 = 1.5
Range: maximum value - minimum value = $3 - $1 = $2
Group B:
$0: * (1 dot)
$1: * * * (3 dots)
$2: * * * (3 dots)
$3: * * * * (4 dots)
$4: * (1 dots)
$5: * * * (3 dots)
Total number of dots: 1 + 3 + 3 + 4 + 1 + 3) = 15
Mode: $4 (the most repeated value)
Mean: [$1 × 3 + $2 × 3 + $3 × 4 + $4 × 1 + $5 × 3 ] / 10 = $40 / 10 = $4
Median: the value of the eigth point = $3
Range: maximum value - minimum value = $5 - 0 = $ 5
Differences:
Mode
Group A: $1
Group B: $4.
Hence, difference is $3
Mean:
Group A: $1.1
Group B: $4
Hence, difference is $ 2.9
Median:
Group A: $1.5
Group B: $ 3
Hence, difference is $1.5
Range:
Group A: $3
Group B: $5
Hence, the difference is $5 - $3 = 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
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