Question

LaTesha and Bernard are playing a game. Their scores for five games are shown in the table below.

LaTesha’s and Bernard’s Scores

LaTesha’s Scores

92

45

67

36

80

Bernard’s Scores

63

68

62

69

53

Which statement comparing the means to the ranges is true?
The means differ by 1, but the ranges differ by 40.
The means differ by 1, but the ranges differ by 2.
The means differ by 5, but the ranges differ by 40.
The means differ by 5, but the ranges differ by 2.LaTesha and Bernard are playing a game. Their scores for five games are shown in the table below.

LaTesha’s and Bernard’s Scores

LaTesha’s Scores

92

45

67

36

80

Bernard’s Scores

63

68

62

69

53

Which statement comparing the means to the ranges is true?
The means differ by 1, but the ranges differ by 40.
The means differ by 1, but the ranges differ by 2.
The means differ by 5, but the ranges differ by 40.
The means differ by 5, but the ranges differ by 2.

Answer 1

To determine which statement is true regarding the differences in means and ranges of LaTesha's and Bernard's scores, we first need to calculate the means and ranges for each player.

**LaTesha's Scores:** 92, 45, 67, 36, 80

1. **Mean of LaTesha's Scores:**
\[
\text{Mean} = \frac{(92 + 45 + 67 + 36 + 80)}{5} = \frac{320}{5} = 64
\]

2. **Range of LaTesha's Scores:**
\[
\text{Range} = \text{Max} - \text{Min} = 92 - 36 = 56
\]

---

**Bernard's Scores:** 63, 68, 62, 69, 53

1. **Mean of Bernard's Scores:**
\[
\text{Mean} = \frac{(63 + 68 + 62 + 69 + 53)}{5} = \frac{315}{5} = 63
\]

2. **Range of Bernard's Scores:**
\[
\text{Range} = \text{Max} - \text{Min} = 69 - 53 = 16
\]

---

**Comparing Means:**
- Mean difference = \(64 - 63 = 1\)

**Comparing Ranges:**
- Range difference = \(56 - 16 = 40\)

Now we summarize our findings:
- The means differ by 1.
- The ranges differ by 40.

The correct statement is:
**"The means differ by 1, but the ranges differ by 40."**