WASHINGTON (CNS) — In the parable of the vineyard in the Gospel of Matthew, “I’m the guy who was hired at 3 o’clock in the afternoon,” said Deacon Michael Fragoso.

A pediatrician for 24 years in central New Jersey, he left his career to enter Blessed John XXIII National Seminary in Weston, Mass., and study to become a priest of the Diocese of Metuchen, N.J.

“The promise ended when my wife died,” he told Catholic News Service, explaining that her death after 31 years of marriage made him a single man again, allowing him to discern what he called a “delayed vocation” to the priesthood.

Deacon Fragoso, who emigrated from Cuba to the United States as a child, was one of four transitional deacons who spoke to CNS in telephone interviews. All will be ordained to the priesthood this summer.

Their vocations illustrate how the age of men feeling the call to the priesthood is gradually increasing, as reported in a new study released by the Center for Applied Research in the Apostolate at Georgetown University in Washington.

According to “The Class of 2013: Survey of Ordinands to the Priesthood,” the average age of men becoming priests this year is 35.5. Released May 1, it is the annual national survey of men being ordained for U.S. dioceses and religious communities.

(See the full report here.)

It is the 17th annual survey of ordinands commissioned by the Secretariat for Clergy, Consecrated Life and Vocations of the U.S. Conference of Catholic Bishops.

About 74 percent of an estimated 500 men to be ordained priests in the United States in 2013 responded to the survey. Three of every 10 were born outside the U.S. The study also showed that before entering the seminary, some of them men worked in education, finance, accounting and insurance.

“A lot of young men are running away … finally when they settle down, they find themselves called to (the priesthood),” Deacon Fragoso said.

“We live in culture right now that is enabling young men to perpetuate their adolescence through entertainment (and) video games,” said Deacon Christopher Gama, a Capuchin brother who studied at St. John Vianney Theological Seminary in Denver.

“(It is) not surprising to me that they’re turning to the priesthood later in life … when those means of engaging are not fulfilling enough,” he said.

“We need to be a little bit more proactive about talking to young people about vocations,” said Deacon Brendan Guilfoil, who studied at Mundelein Seminary in Mundelein, Ill., for the Archdiocese of Chicago.

Deacon Guilfoil, who entered St. Joseph College Seminary just out of high school, said that there are not enough people talking to high school and grade school students about the possibility of becoming a priest.

“When I went to visit the college seminary, it seemed to me that’s where I belonged,” he explained about his discernment process.

Deacon Phillip Ganir, the son of Filipino immigrants originally from Hawaii, agreed. A seminarian at the Jesuit School of Theology of Santa Clara University, he was preparing to be ordained a Jesuit priest.

As a high school student, he was fascinated by the history of the Jesuits he read about in books, and was inspired by the witness of the parish priests whom he served alongside at funerals as an altar boy.

Those priests, who were Capuchins, “were really models of joy for me and they were just beautiful people in many ways,” he said. “My spiritual heroes, they modeled joy and community life to a high school kid.”

Deacon Gama dropped out of Colorado State University, where he was studying civil engineering, because he “felt an interior voice say, ‘Follow me.'” He took Jesus “literally,” he said. After reading about the life of St. Francis, Deacon Gama decided to pursue joining the Capuchin order.

“I thought once you showed up at monastery they just let you come in,” he said. After eight months of coming to know the Capuchin order on a deeper level in Denver, he decided to join. Four years later, he entered the seminary to pursue his “second call” to be a Capuchin priest.

The June 8 ordination of Deacon Ganir will mark 14 years with the Jesuits; the process of priestly formation for Jesuits takes between eight and 14 years. He is excited to continue to serve his superiors as they see fit for the church.

“Even as a musician, I have to be free enough to … forgo music and do something else,” if that is what his superior asks of him, said Deacon Ganir, who plans to continue studies in sacred choral music.

Some sociologists consider “fallen away Catholics” to be the second largest denomination in the U.S., noted Deacon Fragoso.

“Bringing them back to Christ … is the biggest challenge” he said he will face as a new priest.

“Since they’re not coming in the doors we have to go out and find them,” added Deacon Guilfoil.

Priests, Deacon Ganir said, need to provide compelling, sustaining and good reasons in response to the question posed by many: “Why be Catholic?”

There has to be not only a good reason, but a good enough reason to give one’ life to Christ, he said.

In the seminary, Deacon Gama has lived in highly Catholic culture with a lot of support and fraternal friends. “In the secular world, that’s not always the case,” he said, hinting that he was nervous about his first assignment as a civilian chaplain at the Fort Carson Army trauma hospital in Colorado Springs, Colo.

Father Carlos Suarez, ordained a priest of the Boston Archdiocese in May 2011, serves three collaborative cluster parishes. He told CNS that it takes a lot longer to build relationships with people because he is “bouncing around” so much.

Father Suarez had some suggestions for new priests. “Have good friends around you: both priest friends and lay friends,” he said. “Being in a parish, people are … less likely to tell you where things might need to be changed in your own life.”

“Take time for downtime,” he added, explaining that he uses an online calendar and always makes sure to include “‘tab’ time,” or “‘take a break’ time.”